中科院数学与系统科学研究院

数学研究所

学术报告会

报告人： Akhil Mathew(Harvard University / University of Chicago)

题  目：Derived induction and restriction theory

时  间：2017.08.13（星期日），15:30-16:30

地  点：数学院南楼N913室

摘  要：Let G be a finite group. Then it is a classical result of Quillen that the group cohomology of G can be recovered, up to nilpotence, from the cohomology of its elementary abelian subgroups. Using ideas from descent theory, we introduce a class of genuinely equivariant spectra that can be recovered in a strong homotopical sense from their restrictions to a given family of subgroups. We obtain large classes of examples of such equivariant spectra and show in particular show that complex-oriented theories have this property with respect to the family of abelian subgroups. As a result, we obtain (by decategorifying) analogs of the F-isomorphism theorem as well as analogs of Artin and Brauer induction for complex-oriented theories. This is joint work with Niko Naumann and Justin Noel.